LPP

Asked by Anshul Kansal | 25th Apr, 2013, 06:32: PM

Expert Answer:

Let the company produce x type A and y type B belts
 
Also, let the time taken to make type B belts be m hours and hence, the time taken to make type A belt would be 2m hours
 
The total time to make these belts  = 2mx + ym
 
Since, at max the company can make at the most 1000 type B belts per day
 
Hence, in any given day, 2mx+ym <= 1000m
2x+y <= 1000  (1)
 
Also, x<=400 (2) and y<=700 (3)
 
Also, x+y<=800 (4) 
 
Also, x>=0 and y>=0
 
Profit = 2x+1.5y 
We need to maximise profit given the constraints. So, for that draw all the 6 lines on the graph and check the common area, you will form a hexagon ABCDEF with A(0,700); B(100,700); C(200,600); D(400,200); E(400,0); F(0,0)
 
Since the feasible region is a bound region, we can check the profit function at all the vertices to find the point of maxima
 
At point A: 2(0)+1.5(700) = 1050
At point B: 2(100)+1.5(700) = 1250
At point C: 2(200)+1.5(600) = 1300
At point D: 2(400)+1.5(200) = 1100
At point E: 2(400)+1.5(0) = 800
At point F: 2(0)+1.5(0) = 0
 
So, the maxima lies at point C with x = 200 and y = 600 and the maximum profit = Rs 1300.
 

Answered by  | 26th Apr, 2013, 05:39: AM

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